I leave my UV filter on my lens all the time. I never take it off. I guess it is more for protection than filtering. When I use a filter such as an Amber or Red, I simply screw the filter into the UV filter. I do not remove the UV filter.
Is this a suitable way to operate or should I be removing the UV filter when I use different filters?
My suggestion is to go naked and take off the UV filter. Let the lens work the way it was designed to work. Use a lens hood, it will help you far more and is a good way to protect your lens. If you must use a filter, try to use it with a hood as well.
Don't take our word for it, go and make test photos: at night, with strong, overexposed light sources off-center at various places in the frame, without filter and with one or two filters. See if you can find combinations of the factors mentioned above that will give you ghosts or veiling glare. I guess there'll be plenty.